Question

A rectangular hall is 1m long & 6m broad. It's flooring is to be made of square tiles of side 30 cm. How many tiles will fit in the entire hall ? How many would be required if tiles of side 15 cm were used ?

Answer 1

Given: Length of rectangulαr hαll is 1m long & 6m broαd. & its flooring is to be mαde of squαre tiles of side 30cm.

     

Need to Find: The number of tiles thαt will fit in the entire hαll & the number of tiles required if tiles of side 15cm were used.

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❍ As we know thαt:

$\star \; \underline{\boxed{\frak{\purple{Area_{(rectangle)}=Length \times Breadth}}}}$

Therefore,

$:\implies \sf 12 \times 6 \\\\:\implies \underline{\boxed{\frak{ 72 m^2}}} \; \bigstar$

$\boxed{\sf{\purple{1m = 100 cm}}}$

$\boxed{\sf{\purple{30cm = \dfrac{30}{100} m}}}$

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$\sf {Area \; of \; square \; tile = (side)^2} \\\\:\implies \; \sf{\bigg( \dfrac{30}{100} \bigg)^2}\\\\:\implies \; \sf{\dfrac{3\cancel{0}}{10\cancel{0}} \times \dfrac{3\cancel{0}}{10\cancel{0}}}\\\\:\implies \; \sf \dfrac{3}{10} \times \dfrac{3}{10} \\\\:\implies \; \underline{\boxed{\frak{\purple{\dfrac{9}{100} m^2}}}} \; \bigstar$

Therefore,

$\sf The \; number \; of \; tiles \; required = \dfrac{area \; of \; floor}{area \; of \; 1 tile}\\\\:\implies \; \sf{\dfrac{\dfrac{72}{9}}{{100}}}\\\\:\implies \; \sf{\cancel{72} \times \dfrac{100}{\cancel{9}}}\\\\:\implies \; \underline{\boxed{\frak{\purple{800 \; tiles}}}} \; \bigstar$

• If the side of 1 tiles = 15 cm = 15/100 m

$\sf Area~ of ~1 ~tile = (side)^2\\\\:\implies \sf \bigg(\dfrac{15}{100}\bigg)\\\\:\implies \sf \dfrac{\cancel{15}}{\cancel{100}} \times \dfrac{\cancel{15}}{\cancel{100}} \\\\:\implies\underline{\boxed{ \frak{ \dfrac{9}{400} m^2}}} \; \bigstar$

Therefore,

The number of tiles required = (αreα of floor)/(αreα of 1 tile)

$:\implies \sf \dfrac{72}{9} = \cancel{72} \times \dfrac{400}{\cancel{9}}\\\\:\implies \sf 8 \times 400\\\\:\implies \underline{\boxed{\frak{3200 \; tiles}}} \; \bigstar$

$\therefore \underline{\sf{800 \; tiles \; will \; fit \; in \; the \; entire \; hall.}}$

$\therefore \underline{\sf{3200 \; tiles \; will \; be \; required \; if \; tiles \; of \; side \; 15cm \; were \; used.}}$

Answer 2

Answer:

•● ᴀɴsᴡᴇʀ●•

Given that,

Long = 1m

Board = 6m

side of square tiles = 30cm

side of one tile = 15cm

• Area of the Rectangle = Length × Breadth

=> 12 × 6

=> 72m²

• 1m = 100cm

so, 30cm = 30/100m

• Area of square tiles = Side × Side

=> 30/100 × 30/100

=> 3/10 × 3/10

=> 9/100m²

• The number of tiles required

=> Area of floor/Area of tile

=> 72× 100/9

=> 800tiles

• Area of 1 tiles = Side × Side

=> (15/100) × (15/100)

=> 9/400m²

Then,

The number of tiles required

=> Area of floor/Area of 1 tiles

=> 72/9 = 72×400/9

=> 8×400

=> 3200 tiles (Answer)

♡ ᴍɪss_ɪɴɴᴏᴄᴇɴᴛ♡